Identical Twins - Math Can Take You Places

Identical Twins - Math Can Take You Places

LESSON 4
“Identical Twins”
by Nancy Lachowicz
CONCEPT AREA Equivalency
GRADE LEVEL 6
TIME ALLOTMENT 60 minutes
LESSON Students will gain an understanding of equivalency by engaging in different activities. They
OVERVIEW will understand that the quantity or expression on the left side of the equal sign must
equal or represent the same quantity that is on the right. Students will be introduced to
variables, which represent an unknown quantity in an equation. They will also learn how
to solve an equation for the value of the variable.
LESSON Students will brainstorm different forms of equivalency, make a human equivalent
ACTIVITIES problem, work in groups, play the game, “Identical Twins,” create word problems to go
OVERVIEW with equation and do assessment and extension activities.
LEARNING Students will be able to:
OBJECTIVES • Formulate an equation from a problem situation.
• Use letters (variables) to represent an unknown in an equation.
• Generate equivalent forms of fractions, percents and decimals.
• Understand that equivalency is everywhere in “real-world” situations.
STANDARDS From the Texas Essential Knowledge and Skills for Math for grade 6:
(TEKS)
Grade 6
6.1(B), 6.3(B), 6.5(A)
MEDIA Video: Math Can Take You Places #002 “Equivalency”
COMPONENTS
MATERIALS Per Class:
• Twenty four 5” x 8” index cards
• Large “Equal” sign
• “Identical Twins” laminated cards
Per Pair:
• 2 dice or number cubes
• 2 different colored pencils or pens
• “Percent Tic-Tac-Toe” handout
PREP FOR
TEACHERS
• Prepare classroom materials, including index cards.
• Cue video as needed for discussion.
Note:
The concept of fact families will be covered during this lesson. Students may need to
1
LESSON 4
“Identical Twins”
by Nancy Lachowicz
review the concept prior to beginning the activities, especially if your class includes
students who are acquiring English as a second language (ESL).
INTRODUCTORY 1. Generate discussion by taking responses from students regarding the “equal sign”
ACTIVITY: displayed on the front board. Call on three student volunteers to come to the front of
SETTING THE the room. Place two students on the left of the equal sign and one on the right.
STAGE
2. Ask the following guided questions:
a. What have we created?
b. Is it balanced? Why or why not?
c. What needs to be done to demonstrate balance or equivalency? (Take one student
away on the left.)
d. How could we write this as an equivalent expression? (2 - 1 = 1)
e. Explain that rational numbers come in all different forms. You can express them as
fractions, decimals and percents.
Ex:
f.
50
100
= 0.50 or 50%
Think of everyday experiences where you have encountered fractions, decimals
and/or percents (for example: in sports, newspapers, weather reports, etc.).
3. Explain that an integer is any whole number, its opposite and zero. Say that all
integers are rational numbers. Rational comes from the term “ratio.” A rational number
can be written as the ratio a where both a and b are integers and b ≠ 0.
b
The following numbers are all rational numbers as they can be expressed as a ratio in a
form:
b
5 and –21
5 = 5 and -21 = -21
1
1
4. Explain the importance of comparing rational numbers using the following discussion
threads:
a. Checking ratings, etc.
b. Comparing cost
c. Organizing information
d. Collecting and displaying data
5. “When we compare rational numbers, it is easier to compare them if they have
something in common; i.e., a common denominator, decimal form, percent form, etc.”
Examples would include .075 and 7. We would change 0.75 to 75 and
10
100
change 7 to its equivalency 70. We could conclude that 0.75 is the greater
10
100
2
LESSON 4
“Identical Twins”
by Nancy Lachowicz
of the two fractions because when the denominators are the same, we can easily
compare the two numerators and see that 70 is more than 7.
6. We also know that 1 = 100%; therefore, 2 = 200%. To convert a rational number to a
percent, multiply the number by 100.
To write the equivalent form of 4.3 as a percent, multiply by 100:
4.3 · 100 = 430 %
To write the equivalent form of a percent as a rational number, divide the percent by
100:
875% ÷ 100 = 8.75
LEARNING 1. Have students create a word problem that uses these two rational numbers and
ACTIVITIES compares with the inequality sign to show which is larger or smaller.
Examples: Order 5 ¾, 5.8, and 550% from greatest to least:
Hint: Write each rational number in decimal form. Add zeros, so that all have the same
number of decimal places. Compare by looking at place value. Order:
5 ¾ = 5.75
5.8 = 5.80
550% = 5.50
Answer: 5.8 > 5 ¾> 550%
2. Have students create real-life situations to compare their own rational numbers.
3. “Percent Tic-Tac-Toe” is the final activity, or it can be played on a separate day as a
review.
CULMINATING Say: “We are going to play ‘Identical Twins’.” After I shuffle the cards, you will each
ACTIVITY receive a laminated card. When I say ‘go’ you will look at your card and try to find your
identical twin. Every player who finds his/her other twin is a winner.”
CROSS- Math
CURRICULAR
When all matches are found, have each pair of students create a word problem using
EXTENSIONS
their sentence card and giving the answer. Divide the class into two groups and have a
contest to see which team can solve the word problems correctly. Play “Percent TicTac-Toe” game using dice or number cubes.
Language Arts
• Read Shoeless Joe & Black Betsy, by Phil Bildner, illustrated by D. F. Payne.
• Have students research former Olympic athletes and record their statistics using
fractions, decimals and percents. Then, have students present their findings in an oral
presentation.
3
LESSON 4
“Identical Twins”
by Nancy Lachowicz
REAL-WORLD Use a newspaper to locate different forms of numbers that represent equivalency; for
CONNECTIONS example: decimals, percents and fractions.
ASSESSMENT Students will complete the Equivalency Assessment worksheet that is posted in the
handouts.
STUDENT “Identical Twins” Playing Cards
HANDOUTS Equivalency Assessment
“Percent Tic-Tac-Toe”
4
LESSON 4
“Identical Twins”
by Nancy Lachowicz
Identical Twins
Playing Cards
p.1
x = 6y
The sum of
three
consecutive
whole
numbers is 15
x + (x+1) +
(x + 2) = 15
x=y-3
One number
is five more
than another
number
x=y+5
2x + 7 = 15
Double a
number
increased by
8 is 24
2x + 8 = 24
Triple a
number
decreased by
8 is 19
3x - 8 = 19
Forty
increased by a
number is
four times the
number
40 + x = 4x
Double a
number
increased by 4
is 20
2x + 4 = 20
One number
is six times
another
One number
is three less
than another
number
Seven more
than twice a
number is 15
Identical Twins
Playing Cards
p.2
5
LESSON 4
“Identical Twins”
by Nancy Lachowicz
Seventeen is four
more than x
17 = x + 4
Thirty-six is half of
x.
x / 2 = 36
x decreased by
seven is 23
X – 7 = 23
Two more than
twice x is 18
2x + 2 = 18
Eighty-three is 12
less than x
83 = x – 12
The quotient of x
divided by three
is seven
x=7
3
The product of
seven and x is
42
7x = 42
The sum of x and
35 is 85
X + 35 = 83
The difference
of x and 17 is
37
x – 17 = 37
6
LESSON 4
“Identical Twins”
by Nancy Lachowicz
Name_______________________
Equivalency Assessment
1. Recently, a local newspaper reported that 5 out of 20 people watch television less than 2 hours a day. The rest of
the people surveyed said they watch television between 2 and 5 hours per day. Which decimal represents the
number of people who watch between 2 and 5 hours of television a day?
A.
B.
C.
D.
0.75
0.2
0.25
0.6
2. Mr. Jones distributed 64 sheets of graph paper to his geometry class. Each student received 2 sheets of graph paper.
Which equation can be used to find s: the number of students in the class?
A.
B.
C.
D.
s = 64 x 2
s = 64 - 2
s = 64 + 2
s = 64 / 2
3. Order the following from least to greatest:
1/2
0.25
3/5
75/100
_____________________________________
4. On Friday, Lake Rock Middle School reported 25% of their student body absent. What fractional part of the student
body was not absent?
A.
B.
C.
D.
1/4
2/5
1/5
3/4
5. One of the top professional basketball players scored the following points in the last five games: 36, 21, 18, 25, 30.
Which equation could be used to determine the player’s average?
A.
B.
C.
D.
a = (36 + 21 + 18 + 25 + 30) / 5
a = (36 + 21 + 18 + 25 + 30) x 5
a = 2 (36 + 21 + 18 + 25 + 30)
not here
7
LESSON 4
“Identical Twins”
by Nancy Lachowicz
Equivalency Assessment
Answer Key
1. A
2. D
3. 0.25, 1/2, 3/5, 75/100
4. D
5. A
8
LESSON 4
“Identical Twins”
by Nancy Lachowicz
PERCENT TIC-TAC-TOE
16%
100%
40%
80%
50%
25%
50%
20%
25%
66%
83%
40%
33%
75%
60%
33%
75%
20%
16%
25%
20%
16%
100%
40%
40%
100%
75%
50%
20%
25%
66%
50%
60%
33%
75%
60%
Materials: Two 1-6 number cubes (or dice), two different colored pens, calculator (optional)
Objective: Recognize equivalent fractions and percents
Directions: This game is played like Tic Tac Toe. Players take turns tossing the number cubes and
arranging the numbers into a fraction. Each player determines the equivalent percent and circles it on
the Tic Tac Toe grid. If the equivalent percent cannot be found, the player must pass. Players must
calculate the equivalent percent and prove their reasoning. (They may use a calculator if the teacher
chooses.) Play continues until someone gets 3 in a row, column or diagonal. If neither player gets a Tic
Tac Toe, each equivalent percent matched is worth 5 points. Players add up their points to determine
the winner of the game.
9
LECCIÓN 4
“Gemelos Idénticos”
by Nancy Lachowicz
Te Lleva a Muchos Lugares
Nombre__________________________________________________ Fecha____________
Jugando a las Cartas
x = 6y
La suma de tres
números enteros
consecutivos es
15
x + (x+1) +
(x + 2) = 15
x=y-3
Un número es
cinco más que
otro número
x=y+5
2x + 7 = 15
El doble de un
número más 8 es
24
2x + 8 = 24
El triple de un
número menos
8 es 19
3x - 8 = 19
Cuarenta más
otro número es
cuatro veces ese
número
40 + x = 4x
El doble de un
número más 4
es 20
2x + 4 = 20
Un número es
seis veces más
que otro
Un número es
menos tres que
otro número
Siete más un
número
duplicado es 15
1
LECCIÓN 4
“Gemelos Idénticos”
by Nancy Lachowicz
Te Lleva a Muchos Lugares
Diecisiete es
cuatro más que
x
17 = x + 4
Treinta y seis es
la mitad de x.
¿ Esto no
debería ser
x / 2 = 36?
x disminuído
siete es23
X – 7 = 23
El doble de x más
dos es 18
2x + 2 = 18
Ochenta y tres
es x menos 12
83 = x – 12
El cociente de x
dividido entre
tres es siete
El producto de
siete y x es 42
7x = 42
La suma de x y 35
es 85
La diferencia de
x y 17 es 37
x – 17 = 37
2
X
------- = 7
3
X + 35 = 85
LECCIÓN 4
“Gemelos Idénticos”
by Nancy Lachowicz
Te Lleva a Muchos Lugares
Nombre_______________________
Evaluación de la Equivalencia
1. Recientemente, un periódico local informó que 5 personas de cada 20 miran televisión menos de 2 horas por día. El
resto de la gente en la encuesta dice que mira televisión entre 2 y 5 horas por día. ¿Cuál decimal representa el
número de personas que miran televisión entre 2 y 5 horas por día?
A.
B.
0.75
0.2
C.
0.25
D.
0.6
2. El Sr. Jones distribuyó 64 hojas de papel para gráficos en su clase de geometría. Cada estudiante recibió 2 hojas para
gráficos. ¿Cuál ecuación debe ser usada para encontrar el valor de s: el número de estudiantes en la clase?
A.
B.
C.
D.
s = 64 x 2
s = 64 - 2
s = 64 + 2
s = 64 / 2
3. Ordene lo siguiente de menos a mayor:
1/2
0.25
3/5
75/100
_____________________________________
4. El viernes, la escuela intermedia Lake Rock informó que el 25% de sus estudiantes estuvo ausente. ¿Cuál es la parte
fraccional del cuerpo estudiantil que no estuvo ausente?
A.
B.
C.
D.
1/4
2/5
1/5
3/4
5. Uno de los mejores jugadores de baloncesto profesional marcó los siguientes puntos en los últimos cinco juegos:
36, 21, 18, 25, 30. ¿Cuál ecuación puede ser usada para determinar el promedio del jugador?
A.
B.
C.
D.
a = (36 + 21 + 18 + 25 + 30) / 5
a = (36 + 21 + 18 + 25 + 30) x 5
a = 2 (36 + 21 + 18 + 25 + 30)
no está aquí
3
LECCIÓN 4
“Gemelos Idénticos”
by Nancy Lachowicz
Te Lleva a Muchos Lugares
Evaluación de la Equivalencia
Clave de las Respuestas
1) A
2) D
3) 0.25, 1/2, 3/5, 75/100
4) D
5) A
4